# sric: Sharpe Ratio Information Coefficient In SharpeR: Statistical Significance of the Sharpe Ratio

## Description

Computes the Sharpe Ratio Information Coefficient of Paulsen and Soehl, an asymptotically unbiased estimate of the out-of-sample Sharpe of the in-sample Markowitz portfolio.

## Usage

 `1` ```sric(z.s) ```

## Arguments

 `z.s` an object of type `sropt`

## Details

Let X be an observed T x k matrix whose rows are i.i.d. normal. Let mu and Sigma be the sample mean and sample covariance. The Markowitz portfolio is

w = Sigma^-1 mu,

which has an in-sample Sharpe of zeta = sqrt(mu' Sigma^-1 mu).

The Sharpe Ratio Information Criterion is defined as

SRIC = zeta - ((k-1) / (T zeta)).

The expected value (over draws of X and of future returns) of the SRIC is equal to the expected value of the out-of-sample Sharpe of the (in-sample) portfolio w (again, over the same draws.)

## Value

The Sharpe Ratio Information Coefficient.

## Author(s)

Steven E. Pav [email protected]

## References

Paulsen, D., and Soehl, J. "Noise Fit, Estimation Error, and Sharpe Information Criterion." arxiv preprint (2016): http://arxiv.org/abs/1602.06186

Other sropt Hotelling: `inference`
 ``` 1 2 3 4 5 6 7 8 9 10``` ```# generate some sropts nfac <- 3 nyr <- 5 ope <- 253 # simulations with no covariance structure. # under the null: set.seed(as.integer(charToRaw("fix seed"))) Returns <- matrix(rnorm(ope*nyr*nfac,mean=0,sd=0.0125),ncol=nfac) asro <- as.sropt(Returns,drag=0,ope=ope) srv <- sric(asro) ```